MFNAT

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MFNAT

Mono-Frequency Noise Attenuation.

Level: 9737Last update: September 1997

FUNCTION

General

This program attenuates mono-frequency or near mono-frequency noise in a seis-mic trace by adaptively estimating the noise and subsequently subtracting the esti-mated noise from the contaminated trace.

The program is most effective when the noise is strong and completely dominatesthe underlying signal; in those circumstances the program will remove more noiseand is less likely to damage the signal than other approaches such as notch-filteringor spectral whitening.

MFNAT is a single channel process that attenuates mono-frequency or pseudomono-frequency noise. The program can be used, for example, to remove power-line noise from land data or pseudo mono-frequency noise from data acquired inmarsh or shallow water areas.

The noise is estimated and subtracted from the contaminated trace by a process cal-led adaptive noise cancellation (ANC). The program is able to adapt to variations inthe noise frequency along the trace or from trace to trace, and can therefore be moreeffective, and do less damage to the underlying signal, than techniques such asnotch filtering

The module requires an estimate of the noise frequency as input for an optimal noisecancellation.

The input is a mono-frequency noise corrupted trace and the frequency of the noise.The output is the trace with noise removed.

Geocluster User’s Manual MFNAT 1

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FUNCTION CALL

Description

Column Content

1 *

3-7 MFNAT

15-16 Input buffer: contains trace to be processed

23-24 Output buffer: contains processed trace

31-80 Parameters

Parameters

General process parameters

Mandatory parameter

FINITf f = Initial guess for the noise frequency.Supply a value that is as close as possible to the average frequencyof the noise throughout the data. Integer.f > 0. (Hz).

Optional parameter

METHODi Method used for noise attenuation:

i = 1: f is constant along the traces (recommended for power linenoise).

i = 2: f varies along the traces in the data (recommended for swampnoise).

By default, i = 1.

See the “Technical Description” and “RECOMMENDA-TIONS” for more information on this parameter.

Optional processing window parameters

The processing window should be chosen as long as possible in order to permit thealgorithm to converge optimally to the noise, and noise must dominate in most ofthe window.

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Wa-Wb a = Start of the processing windowb = End of the processing windowa and b in ms. Integer.0 a < bBy default all the trace is processed.

The processing window starts at the value of Wa and it ends at the computed starttime plus the value of (Wb-Wa), or at the last live sample on the trace if sooner.

Data outside the processing window is unchanged by this program.

Research parameters

These parameters are for RESEARCH PURPOSES ONLY and should not be spe-cified during normal processing.

NHARMi i = Number of harmonics of the base frequency (FINIT) to suppressif such harmonics are present in the data. By default, i = 1 (i.e. pro-cess only the base frequency).Integer. i 1.

FBACKb b = Feedback gain.0 < b 1.By default, b = 0.01.

LDIAG Parameter for diagnostic print.Caution: if specified, large quantities of printout may be generated.


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TRACE HEADER

Status of the output trace header

The program does not change the values of the trace header words.

1 2 3 4 5 6 7 8 9 0

WORDS 1 to 10

WORDS 11 to 20

WORDS 21 to 30

WORDS 31 to 40

WORDS 41 to 50

WORDS 51 to 60

WORDS 61 to 64


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RECOMMENDATIONS

Noise types

The application domain of MFNAT is the elimination of mono-frequency or pseudomono-frequency noise. The first kind of noise is encountered in land data mostlyfrom power line interference. The second kind of noise may be present in dataacquired in shallow water environments such as marsh or swamp areas. In this casethe noise originates from trapped waves in the water layer.

Power line noise

Power line noise is electrical interference that is due to the presence of a nearbyelectrical power supply. It is characterised by a mono-frequency noise train that ispresent at all times on the trace, and which has a close to constant frequency andamplitude on the trace. The amplitude can vary greatly, however, from trace totrace and from shot record to shot record.

Whilst notch filtering or spectral whitening are often used to remove this noise type,it can be removed more effectively and with less damage to the underlying signalby adaptive noise cancellation as implemented in this program. The basic noiseremoval algorithm, METHOD=1, (the default option) is recommended in this case.

Swamp noise

When seismic data is recorded in marsh or shallow water areas it is possible for thedata to be contaminated with long pseudo mono-frequency noise trains that are cau-sed by trapped waves in the near-surface. (This noise is an extreme form of the longdispersed wave trains sometimes seen in marine surveys when interference noisefrom other seismic crews is present.)

The frequency of this type of noise varies slightly in time along the seismic traces,but also can vary considerably from place to place in the data. In this case it isrecommended to apply METHOD=2 in MFNAT, since this version of the algorithmcan tolerate variations of the noise frequency around the value of the initial fre-quency FINIT. The value of FINIT in this case should be chosen close to the ave-rage frequency of the noise throughout the data. Tests have shown that MFNAT isable to tolerate variations of frequency along the trace or from place to place of asmuch as ±5 Hz; see Example 2 and Example 3 .


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Feedback gain (research parameter)

If the results obtained using the general process parameters are inadequate it maybe possible to improve them in some cases using the feedback gain research para-meter FBACK. Particularly in the case of pseudo mono-frequency noise or swampnoise (see above) an improved result can sometimes be obtained using an increasedvalue for this parameter. Increasing the value of FBACK may however causedamage to the underlying signal, and this parameter should therefore be used withcare. Values between 0.01 and 0.05 have been found to be effective; values greaterthan 0.05 should not be used.


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EXAMPLES

The performance of the module MFNAT is demonstrated in the following Geovec-teur jobs.

In the first example the module is applied using METHOD=1 on a land shot contai-ning mono-frequency noise of 51 Hz. (The noise frequency was determined fromthe amplitude spectra of the traces using EXAM.)

In the second example a synthetic sweep with frequencies between 49Hz and 51Hzwas added to these data and MFNAT is applied using METHOD=2.

In the third example MFNAT’s performance is compared with notch filtering inremoving noise whose frequency changes slightly from trace to trace.

Example 1

********************************************************************** DLOOP 1* RUNET AA FILE=r24sl-f:+ FILE=/proj/6442/1326442/JOBS/MFNAT/shot197.cst,*** Adaptive noise cancellation* MFNAT AA AB FINIT51,W0-W4000,* WUNET AB FILE=r24sl-f:+ FILE=/proj/6442/1326442/JOBS/MFNAT/anc.cst,* ENDLP********************************************************************** PROCS X(YB1)

Result

The result of example job 1 is shown in the following pages.

Figure 1 shows the original shot record with the 51Hz mono-frequency noise.Application of MFNAT produces the noise removed record in Figure 2 .Figure 3 shows the difference between Figure 1 and Figure 2 , i.e. the removednoise.


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Figure 1Shot record from land data containing mono-frequenct noise of 51 Hz.

The noise frequency was determined from the amplitude spectra of the traces.


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Figure 2The shot record of Figure 1 after application of MFNAT


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Figure 3The difference between Figures 2 and 1, showing the removed noise


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Example 2

In this job “swamp noise” is simulated by adding a synthetic sweep with frequenciesbetween 49Hz and 51Hz to the result of the first example (Figure 2 ). This noiseis then removed by MFNAT using METHOD=2.

********************************************************************** DLOOP 1* DAGEN VS BB RL4000,SI4,FD49,FF51,A8000,NT1,TAP0,* ENDLP********************************************************************** DLOOP 2* RUNET AA FILE=r24sl-f:+ FILE=/proj/6442/1326442/JOBS/MFNAT/anc.cst,*** Add generated noise* EVERY AD AA EE IS1=BB,* WUNET EE FILE=r24sl-f:+ FILE=/proj/6442/1326442/JOBS/MFNAT/shot197_noise.cst,*** Adaptive noise cancellation* MFNAT EE EF FINIT50,W0-W4000,METHOD2,* WUNET EF FILE=r24sl-f:+ FILE=/proj/6442/1326442/JOBS/MFNAT/anc_M2.cst,* ENDLP********************************************************************** PROCS 1B1+X(YB2)

Result

The following pages show the result of Example 2 .

Figure 4 shows the shot record of Figure 2 containg the simulated swamp noise.

The result after application of MFNAT with METHOD=2 is shown in Figure 5 .The difference between Figure 4 and Figure 5 , i.e. the removed noise, is shownin Figure 6 .


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Figure 4The shot record of Figure 2 with added synthetic “swamp noise” (pseudo mono-frequency noise).

The noise frequency varies between 49Hz and 51Hz down the seismic traces.


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Figure 5The shot record of Figure 4 after application of MFNAT with METHOD=2


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Figure 6The difference between Figures 4 and 5, showing the noise removed


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Example 3 : Adaptive noise cancellation versus notch filtering

The experiment of Example 2 was repeated with four different frequency intervalsfor the added noise: 24-26Hz, 26-28Hz, 28-30Hz and 30-32Hz. MFNAT withMETHOD=2 was applied with a global initial frequency FINIT=25HZ in each case.

The MFNAT results for one selected trace are shown in Figure 7 .

Traces 2 to 5 show the result of MFNAT on each of the different noise frequencyranges. Trace 6 is the noise free trace and Trace 1 is the noise contaminated tracefor one of the frequency ranges (24-26Hz).

These results show that MFNAT can tolerate a variation of the noise frequency of±5 Hz away from the initial value and still give satisfactory results.


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Figure 7Swamp noise removal using MFNAT

1 (1) A seismic trace containing simulated “swamp-noise” – a long, ringing,noise train that varies, in this case, from 24Hz at the beginning of the trace to26 Hz at the end of the trace.

2 The result of applying MFNAT to trace (1) using METHOD2 with FINIT = 25Hz; other parameters were allowed to default. A significant proportion of thenoise has been removed from the trace. (Compare this result with trace (6),which is the original noise-free trace.

(3-5)The result of applying MFNAT, with the same parameters as in trace (2), totraces containing noise that varies from 26 to 28 Hz, 28 to 30 Hz and 30 to 32 Hzrespectively from the beginning to the end of each trace. This simulates the resultsthat would be obtained if the swamp noise varied from place to place, due to chan-ges in near-surface conditions. MFNAT is able to adapt to the frequency changesand remove most of the noise in each case.

(6)The original noise-free trace used to construct the noise-contaminated synthetictraces.


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The results in Figure 8 show on the other hand that filtering noise removal usinga notch filter covering the whole bandwidth of the noise, i.e. 24-32Hz, is less effec-tive than MFNAT in removing the noise and preserving the signal. Although itmight be possible to improve this result by increasing the width of the notch beyondthe bandwidth of 10 Hz used here this could potentially be very damaging to thedata.

Figure 8Swamp noise removal using notch filtering

.

1 A repeat of trace (1) of Figure 8, showing a trace containing simulated “swamp-noise” in the frequency range 24 to 26 Hz.

2 The result of applying notch filtering to trace (1). The notch filter was full-onat 24 Hz, full-off at 28 Hz, and full-on again at 32 Hz. Only a small proportionof the noise has been removed. (Compare this result with trace (6), the originalnoise-free trace.)

(3-5)The result of applying notch filtering, with the same parameters as in trace (2),to traces containing noise varying from 26 to 28 Hz, 28 to 30 Hz and 30 to 32 Hzrespectively from the beginning to the end of each trace. Although the notch-filte-


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ring is effective for traces (3) and (4), it does a poor job of removing the noise intraces (2) and (5). It would be possible to improve this result by increasing thewidth of the notch filter, at the risk however of damaging the underlying signal.

(6) The original noise-free trace used to construct the noise-contaminated synthetictraces.


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APPENDICES

Technical Description

Mono-frequency or pseudo mono-frequency noise appears in land data from powerline interference or in shallow water or marsh operations from trapped waves.MFNAT attenuates this kind of noise by adaptive noise cancellation (ANC). SeeWidrow and Stearns, 1985, and Kretschmer et al., 1978, for a detailed analysis ofthis technique, and Dragoset, 1995, or Griffith, 1988, for applications to geophysi-cal problems.

Adaptive noise cancellation

The principle of adaptive noise cancellation is to estimate the amplitude and phaseof the noise from the contaminated seismic trace and to then subtract this estimatednoise from the trace. The estimation process is called adaptive since it is adjustedby a feedback loop from the input data. Typically an algorithm first has a “trainingphase” in which an initial estimate of the model parameters is obtained, and then an“application phase” in which the estimated noise model is subtracted from the data.(In that sense, the process is similar to a neural net; it can be shown to be mathema-tically equivalent to a one-layer net.)

The model of the seismic data at a sample k is D(k) = S(k)+N(k) where S(k) is thesignal and N(k) the noise. For mono-frequency noise or pseudo mono-frequencynoise the noise is represented by

where C is the amplitude, F the frequency, ∆T the sampling interval and ϕ the phaseof the noise. The noise can also be written as:

with

The basic principle of ANC is to estimate the parameters of the noise model (C andϕ or equivalently A and B) by updating the model from sample to sample along theseismic trace. The details of this procedure are given in Figure 9 . For each samplek, the noise model ν(k) is subtracted from the input D(k) to form ERR(k) = D(k) –ν(k) which can be interpreted as an error function for the noise estimate. The noisemodel is then updated in order to decrease the squared error function. This modelupdate is obtained by using the gradient of the squared error as follows:

v k( ) C 2πFk∆T ϕ+( )sin=

v k( ) A 2πFk∆T( )cos B 2πFk∆T( )sin+=

A C ϕsin= and B C ϕcos=

A k 1+( ) A k( ) FBACK gradA

ERR2k( )[ ]⋅–=


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with the gradients

Since the model is updated in a feedback loop, FBACK has the function of a feed-back gain factor.

The basic implementation of ANC that is provided in this program (method 1) usesthe feedback loop of Figure 9 to estimate only the amplitude and phase of thenoise from the data, while the noise frequency F is held equal to an input value sup-plied by the user. An alternative implementation is provided (method 2) in whichslow changes in the noise frequency about the user-supplied value are estimatedfrom the data.

Figure 9Feedback loop for adaptive noise cancellation (ANC).

B k 1+( ) B k( ) FBACK gradB

ERR2k( )[ ]⋅–=

gradA

ERR2k( )[ ] 2– ERR k( ) 2πFk∆T( )cos=

gradB

ERR2k( )[ ] 2– ERR k( ) 2πFk∆T( )sin=

D(k) = S(k) + N(k) ERR(k) = [D(k) - v(k)]+S

noise modelv k( ) A 2πFk∆T( )cos B 2πFk∆T( )sin+=

A = 0B = 0F = FINIT

A A 2FBACK ✳ERR k( ) ✳ 2πFk∆T( )cos+¨B B 2 FBACK ✳ERR k( ) ✳ 2πFk∆T( )sin+¨

FBACK

OUTPUT(k) =D(k) - v(k)

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The values A=0, B=0 and F=FINIT are initial values of the program.


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REFERENCES

Dragoset, B., 1995, Geophysical applications of adaptive-noise cancellation: 65thAnn. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1389-1392.

Griffith, P.G., 1988, Nonlinear Quadrature Noise Canceling of Narrow-BandSignals in Seismic Data: 58th Ann. Internat. Mtg., Soc. Expl. Geophys., ExpandedAbstracts, 1270-1274.

Kretschmer, F.F., and Lewis, B.L., 1978, An improved algorithm for adaptive pro-cessing: IEEE Trans. on Aerospace and Electronic Systems, Vol. AES-14, No.1.

Widrow, B., and Stearns, D., 1985, Adaptive signal processing: Editor: Oppenheim,A. V., Prentice-Hall Signal Processing Series.


MFNAT

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